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Land degradation and desertification in arid and semi-arid areas is of great concern. Accurately mapping percentage vegetation cover (PVC) of the areas is critical but challenging because the areas are often remote, sparsely vegetated, and rarely populated, and it is difficult to collect field observations of PVC. Traditional methods such as regression modeling cannot provide accurate predictions of PVC in the areas. Nonparametric constant k-nearest neighbors (Cons_kNN) has been widely used in estimation of forest parameters and is a good alternative because of its flexibility. However, using a globally constant k value in Cons_kNN limits its ability of increasing prediction accuracy because the spatial variability of PVC in the areas leads to spatially variable k values. In this study, a novel method that spatially optimizes determining the spatially variable k values of Cons_kNN, denoted with Opt_kNN, was proposed to map the PVC in both Duolun and Kangbao County located in Inner Mongolia and Hebei Province of China, respectively, using Landsat 8 images and sample plot data. The Opt_kNN was compared with Cons_kNN, a linear stepwise regression (LSR), a geographically weighted regression (GWR), and random forests (RF) to improve the mapping for the study areas. The results showed that (1) most of the red and near infrared band relevant vegetation indices derived from the Landsat 8 images had significant contributions to improving the mapping accuracy; (2) compared with LSR, GWR, RF and Cons_kNN, Opt_kNN resulted in consistently higher prediction accuracies of PVC and decreased relative root mean square errors by 5%, 11%, 5%, and 3%, respectively, for Duolun, and 12%, 1%, 23%, and 9%, respectively, for Kangbao. The Opt_kNN also led to spatially variable and locally optimal k values, which made it possible to automatically and locally optimize k values; and (3) the RF that has become very popular in recent years did not perform the predictions better than the Opt_kNN for the both areas. Thus, the proposed method is very promising to improve mapping the PVC in the arid and semi-arid areas. [ABSTRACT FROM AUTHOR]